Initial layer and relaxation limit of non-isentropic compressible Euler equations with damping

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Wu, Fuzhou^1,2 

[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[2] Harvard Univ, Ctr Math Sci & Applicat, Cambridge, MA 02138 USA

关键词: Non-isentropic Euler equation with damping;    Relaxation limit;    Ill-prepared data;    Initial layer;    Strong convergence rate;   

DOI  :  10.1016/j.jde.2015.11.034

来源: Elsevier

【 摘 要 】

In this paper, we study the relaxation limit of the relaxing Cauchy problem for non-isentropic compressible Euler equations with damping in multi-dimensions. We prove that the velocity of the relaxing equations converges weakly to the velocity of the relaxed equations, while other variables of the relaxing equations converge strongly to the corresponding variables of the relaxed equations. We prove that as relaxation time approaches 0, there exists an initial layer for the ill-prepared data, the convergence of the velocity is strong outside the layer; while there is no initial layer for the well-prepared data, the convergence of the velocity is strong near t = 0. The strong convergence rates of all variables are also estimated. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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